Question

archimedes could find the purity of a kings crown using buoyancy.how

Answer 1

King Hiero II had a crown in the shape of laurel wreath and Archimedes was asked to check the purity of the crown without damaging it. King wanted to check if the goldsmith has added silver into the crown or not. Now Archimedes could not melt it in order to determine the density. He went to took bath and realised that when he got into the bath tub, the water level rose. He used this to calculate the volume of the crown. Since water cannot be compressed, so when a solid is submerged in water, it will displace experience some buoyant force and some water is displaced which is equal to its own volume. Density of crown can then be calculated by dividing the weight of the crown by volume of the water displaced. If some less dense metal is added, the density of the crown would be lower than that of gold. So in this way he could check the purity of the crown. 
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